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svlad2 [7]
3 years ago
10

Solve the following problem by defining your variables and writing a system of equations:

Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

Answer:

1 donut and a bag of coffee costs $4.50

Step-by-step explanation:

Start by creating a pair of simultaneous equations.

Let x = a donut.

Let y = a bag of coffee.

Therefore:

8x+2y=18

3x+y=7.50

There are a few ways to solve these equations. This time I'll show you the elimination method. We eliminate one of the variables to get the other variable equal to a number.

Start by multiplying one of the equations by a number so that one of the variables has the same coefficient (number at the front) as the same variable in the other equation.

I'll multiply the second equation by 2 so that the y will have a coefficient of 2 like the 1st equation.

2(3x+y)=2(7.50), 6x+2y=15.

Now we have two equations with the same coefficient of y. We can subtract the equations from each other to eliminate the y variable and leave x equal to a number.

Subtracting  8x+2y=18 and 6x+2y=15 :

8x+2y-(6x+2y)=18-(15)

Simplify to get 2x=3.

Therefore x = 1.5.

Now we have one of the variables, we can find the other variable by putting the known variable back into one of the equations.

3x+y=7.50 - original equation

3(1.50)+y=7.50 - substituting x.

4.50 +y=7.50 - simplifying

y=3 - re-arranging to solve for y

Therefore, x=1.5 and y=3.

So 1 donut costs $1.50 and 1 bag of coffee costs $3.

1 donut and a bag of coffee costs $4.50

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